CN104050631A - Low-dose CT image reconstruction method - Google Patents
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Abstract
The invention provides a low-dose CT image reconstruction method. The low-dose CT image reconstruction method comprises the following steps that (1) projection data of equal-slope increments with different projection angles theta are obtained; (2) the projection data are corrected; (3) Fourier transform is conducted on the corrected projection data so that the corrected projection data can be converted into frequency domain spatial data in a polar coordinate system; (4) the frequency domain spatial data in the polar coordinate system are converted into frequency domain spatial data in a pseudo-polar coordinate system; (5) repeated conversion between the frequency domain space in the pseudo-polar coordinate system and the time domain space in a Cartesian coordinate system is conducted on the frequency domain spatial data obtained in the step (4) through the iteration method until the preset final condition is met; (6) a time domain image meeting the final condition is output. By the adoption of the low-dose CT image reconstruction method, the quality of a reconstructed image is guaranteed, and the radiation dose borne by a sample can be effectively reduced.
Description
Technical field
The present invention relates to a kind of image rebuilding method, relate in particular to a kind of low dosage CT image rebuilding method.
Background technology
Computer tomography (Computer Tomography, CT) be a kind of effectively harmless three-dimensional detection technique, it can solve sectional slice from the two-dimensional projection of sample, realize three-dimensional visualization, in the scientific domains such as medical science, materialogy, geophysics, archaeology and biology and industrial nondestructive testing field, play an important role.Referring to Fig. 1 and 2, typical CT imaging system comprises radiation source (collimated beam 110, fladellum 210 and cone-beam) and the detector (planar detector 130 and on-plane surface detector 230) with certain penetration capacity, sample stage 120 between the two, by the relative rotation (rotation center O) between sample and radiant rays and detector, obtain the projected image 140 of sample different angles, then projected image is inputted to computing machine 150, by image reconstruction algorithm, calculate sectional slice, rebuild image 160.Wherein radiation source comprises X ray, gamma rays, neutron, proton, electronics, sound wave and ion beam etc.
For traditional medical X-ray CT and fluoroscopic visualization, controlling radiation dose is a key issue must considering, and the radiation dose that patient is subject to is linear approximate relationship along with obtaining projection number, and accepting for a long time ionising radiation has increased the injury to patient.In addition, for electron microscope technique, because sample must be placed on substrate, cause the projection of some angle to get, finally cause the reduction of reconstructed results resolution.
In traditional CT method for reconstructing, data for projection is to obtain according to the mode of equal angles increment, be that different projections forms a polar coordinate system, and sectional slice to be reconstructed is Cartesian coordinates, therefore in data reconstruction processes, inevitably use interpolation, thereby increased the error of reconstructed results, reduced resolution and the signal to noise ratio (S/N ratio) of reconstructed results.
The most widely used in traditional CT method for reconstructing is filtered back projection (FBP), the method be easier to realize and reconstruction speed fast, but when projection angle is incomplete, filtered back projection often can not provide satisfied result.Simultaneously because the method is used interpolation algorithm in back projection's process, in reconstructed results, can inevitably there is artifact, finally cause the reduction of picture quality, the more important thing is, FBP algorithm needs a large amount of projection angles, make the larger radiation dose of sample reception in data acquisition, in Medical CT application, will bring radiation injury to person under inspection.Other CT reconstruction algorithm, as algebraic reconstruction algorithm (ART) and expectation-maximization algorithm (EM) etc., although can effectively solve the incomplete problem of projection angle, and can utilize a small amount of projection to realize image reconstruction, effectively reduce the radiation dose that sample is subject to, but its process of reconstruction only relates to cartesian coordinate system and polar coordinate system, thereby interpolation that need to be a large amount of, reduced the accuracy of reconstructed results, the speed of simultaneously rebuilding is slow, has limited its usable range.
Summary of the invention
For the defect existing in above-mentioned prior art, the object of the present invention is to provide a kind of low dosage CT image rebuilding method, when guaranteeing reconstructed image quality, can also effectively reduce the suffered radiation dose of sample.
To achieve these goals, the present invention adopts following technical scheme:
A low dosage CT image rebuilding method, the method comprises the following steps:
Step (1), obtains the data for projection that waits slope delta of different projection angle θ;
Step (2), revises described data for projection;
Step (3), carries out Fourier transform to revised described data for projection, so that it converts the frequency domain spatial data under polar coordinate system to;
Step (4), becomes the frequency domain spatial data under pseudo-polar coordinate system by the frequency domain Conversion of Spatial Data under described polar coordinate system;
Step (5), by process of iteration make frequency domain space under pseudo-polar coordinate system of described frequency domain spatial data in described step (4) and time repeat conversion between domain space, until meet default final condition;
Step (6), time-domain diagram picture when output meets final condition.
Further, the described data for projection in described step (1) is the data by waiting slope incremental mode to obtain.
Further, the data that the described data for projection in described step (1) is the slope delta such as approximate that obtained and selected from the data of obtaining by equal angles incremental mode.
Preferably, the described projection angle θ in described step (1) meets following formula:
Wherein, the pixel that N * N is image to be reconstructed.
Preferably, the data of the described data for projection in described step (1) for gathering under collimated beam radiation source.
Further, the described data for projection in described step (1) for gathering and be converted to the data of parallel projection under fladellum or cone-beam radiation source.
Further, described step (1) comprises by shuffle algorithm, the data that gather are converted to the data of parallel projection under described fladellum or cone-beam radiation source.
Further, described step (2) realizes correction by described data for projection is carried out to normalization, zero padding, registration and/or phase place recovery operation.
Preferably, the described Fourier transform in described step (3) is Fast Fourier Transform (FFT), Nonuniform fast Fourier transform or Fourier Transform of Fractional Order.
Aforementioned a kind of low dosage CT image rebuilding method, wherein, described step (5) comprises the following steps:
Step (51), carries out contrary pseudo-polar coordinates Fast Fourier Transform (FFT) to the frequency domain spatial data under described pseudo-polar coordinate system, so that it converts time domain spatial image to;
Step (52), judges whether to meet described default final condition, if met, carries out described step (6), otherwise, execution step (53);
Step (53), revises the described time domain spatial image in described step (51);
Step (54), the described time domain spatial image that described step (53) is revised converts the frequency domain spatial data under pseudo-polar coordinate system to;
Step (55), revises the frequency domain spatial data under the described pseudo-polar coordinate system in described step (54), then returns to step (51).
Further, described step (54) comprises described time domain spatial image is carried out to pseudo-polar coordinates Fast Fourier Transform (FFT).
Aforementioned a kind of low dosage CT image rebuilding method, described step (54) comprises the following steps:
Step (541), calculates the data for projection of each projection angle according to described time domain spatial image;
Step (542), revises the described data for projection in described step (541);
Step (543), the described data for projection that described step (542) is revised is carried out Fourier transform, so that it is converted to the frequency domain spatial data under polar coordinate system;
Step (544), becomes the frequency domain spatial data under pseudo-polar coordinate system by the frequency domain Conversion of Spatial Data under the described polar coordinate system in described step (543).
Preferably, the described Fourier transform in described step (543) is Fast Fourier Transform (FFT), Nonuniform fast Fourier transform or Fourier Transform of Fractional Order.
Preferably, described step (53) is revised described time domain spatial image by exercise boundary constraint condition, Condition of Non-Negative Constrains, real number constraint condition, extreme value constraint condition and/or filtering.
Aforementioned a kind of low dosage CT image rebuilding method, described step (55) is revised the frequency domain spatial data under described pseudo-polar coordinate system by constraint condition and the filtering carried out based on experimental data, wherein, the constraint condition of described execution based on experimental data be utilize in described step (1), obtain the corresponding pseudo-polar coordinate system of data for projection under frequency domain spatial data replacement step (54) in the frequency domain spatial data of the corresponding angle that calculates.
Aforementioned a kind of low dosage CT image rebuilding method, wherein, the described default final condition in described step (52) is at least one in following condition:
The maximum times of described step (5) circulation;
The numerical range of one image parameter;
The minimum value of error function; And
Described error function no longer reduces with iterations increase,
Wherein, described error function is frequency domain spatial data under the described pseudo-polar coordinate system calculating in described step (54) the resulting error function of comparing with the frequency domain spatial data under the corresponding pseudo-polar coordinate system of data for projection of obtaining in described step (1).
Compared with prior art, the present invention has following beneficial effect:
1, method for reconstructing of the present invention is changed between Cartesian coordinates, polar coordinates and three coordinate systems of pseudo-polar coordinates,, the slope delta data for projection such as first obtain, recycling Fourier transform is mapped to the frequency domain space under polar coordinate system by this data for projection, then utilize Fourier to cut into slices theorem sits down the frequency domain Conversion of Spatial Data under polar coordinate system frequency domain spatial data for the pseudo-utmost point, finally make the time domain space iteration back and forth under the frequency domain space of this frequency domain spatial data under pseudo-polar coordinate system and cartesian coordinate system, thereby realize time domain spatial image reconstruction.Because iterative process is to carry out between cartesian coordinate system and pseudo-polar coordinate system, and have accurate Fourier transform relation between these two coordinate systems, therefore process of reconstruction of the present invention does not need interpolation algorithm, has improved the accuracy that CT rebuilds image.
2, traditional filter back-projection algorithm utilizes the data for projection of different angles to carry out interpolation arithmetic to realize reconstruction, therefore the data for projection of large measuring angle need to be obtained and satisfied image reconstruction could be realized, and for a small amount of projection and the incomplete data for projection of angle, can not obtain satisfied result.The present invention is directed to the incomplete data for projection of a small amount of projection and angle, can by frequency domain space and time domain space the computing that iterates the data that lack angle are restored, in process of reconstruction, can avoid interpolation arithmetic simultaneously, therefore can realize the quality image reconstruction of a small amount of incomplete projections.
3, radiation dose and projection number are linear approximate relationship, and the present invention can utilize data for projection still less to realize high-quality image reconstruction, thereby can effectively reduce the radiation dose that sample is subject to.Compare with traditional filter back-projection algorithm, guaranteeing that on the basis of same reconstruction quality, radiation dose can effectively reduce more than 60%.
4, the present invention can use data for projection still less to realize image reconstruction, therefore the present invention can effectively shorten the acquisition time of data for projection.
Accompanying drawing explanation
Fig. 1 is the CT image-forming principle schematic diagram of collimated beam projection;
Fig. 2 is the CT image-forming principle schematic diagram of fladellum projection;
Fig. 3 is polar lattice point schematic diagram;
Fig. 4 is the process flow diagram of image rebuilding method of the present invention;
Fig. 5 A is the former figure based on collimated beam projection of the example 1 according to the present invention;
Fig. 5 B is the sinogram based on collimated beam projection of the example 1 according to the present invention;
Fig. 5 C is the reconstruction figure of the iteration 20 times of the example 1 according to the present invention;
Fig. 5 D is the reconstruction figure of the iteration 100 times of the example 1 according to the present invention.
Fig. 6 A is the reconstruction figure according to the filtered back projection technique of prior art;
Fig. 6 B is the reconstruction figure of the example 2 according to the present invention;
Fig. 7 A is the former figure based on fladellum projection of the example 3 according to the present invention;
Fig. 7 B is the sinogram based on fladellum projection of the example 3 according to the present invention;
Fig. 7 C is the reconstruction figure of the iteration 20 times of the example 3 according to the present invention.
Embodiment
Below with reference to the accompanying drawings, provide preferred embodiment of the present invention, and be described in detail, enable to understand better function of the present invention, feature.
Low dosage CT image rebuilding method of the present invention can be applicable to multiple CT imaging system, for example, Medical CT, the micro-CT of X ray, transmission electron microscope, Single Photron Emission Computed Tomograph (SPECT), positron emission CT(PET) etc., as shown in Figure 4, method of the present invention specifically comprises the following steps:
Step (1), that obtains different projection angles waits slope delta data for projection;
Step (2), revises described data for projection;
Step (3), carries out Fourier transform to revised described data for projection, so that it converts the frequency domain spatial data under polar coordinate system to;
Step (4), becomes the frequency domain spatial data under pseudo-polar coordinate system by the frequency domain Conversion of Spatial Data under described polar coordinate system;
Step (5), by process of iteration make frequency domain space under pseudo-polar coordinate system of frequency domain spatial data under the described pseudo-polar coordinate system in described step (4) and time repeat conversion between domain space, until meet default final condition;
Step (6), time-domain diagram picture when output meets final condition.
In step (1), the data for projection of described different angles can be according to waiting slope incremental mode to obtain, the described slope delta that waits refers to that the difference of the tangent of a upper angle and the tangent of next angle is constant in same group of angle combination (horizontal combination or vertical cartel).
Typically, under polar coordinate system as shown in Figure 3, the straight line that A00 is corresponding and lattice point represent that projection angle is the corresponding projection of 0 degree, the projection of corresponding-45 degree of A11, the projection of corresponding 45 degree of A12, the projection of corresponding 135 degree of A13.Meanwhile, the data for projection lattice point corresponding with A13 due to A11 overlaps, and data are symmetrical, therefore in experiment, only obtain one of them projection, and the present embodiment selects to obtain corresponding-45 degree projections of A11.
Therefore, suppose that the pixel of reconstruction faultage image is N * N, in Fig. 3, according to counterclockwise, the projection angle between A11 to A12 meets formula: θ=-arctan[(N+2-2n)/N], wherein, n=1,2 ..., N; Projection angle between A12 to A13 meets formula: θ=90 °-arctan[(3N+2-2n)/N], wherein, n=N+1, N+2 ..., 2N.Data between data for projection between A13 to A11 and above-mentioned A11 to A13 are symmetrical, thus in the present embodiment without obtaining this part corresponding projection angle.
Preferably, in experiment, not obtain 2N angle, and only obtain a part of angle wherein, in the present embodiment, select to obtain N/4 projection angle.The N/4 an obtaining projection angle, with respect to 2N full angle, can be evenly to choose from 2N full angle, can be also non-homogeneous choosing.
Certainly, described data for projection also can obtain according to traditional equal angles incremental mode, but can only from described data for projection, choose the approximate corresponding data for projection that waits slope delta.Wherein, the scheme of approximate data for projection such as slope delta such as grade of selecting from equal angles increment data for projection of the present invention is as follows:
The projection number of supposing equal angle projection's data is M, projection angle matrix is Ang=[0,180 °/M, 2 * 180 °/M, ..., 180 ° of-180 °/M], Ang(i) i element in representing matrix Ang, tomo(Ang(i)) represent i the data for projection that angle is corresponding in equal angle projection's sequence.
Suppose that faultage image to be reconstructed size is N * N pixel, TOMO(θ n) expressions wait n the data for projection that angle is corresponding in slope projection sequence, the satisfied following formula of θ n wherein:
if Ang(i) satisfied condition | θ
n-Ang (i)+45 ° |=min| θ
n-Ang+45 ° | (wherein θ n-Ang represents all elements comparison in θ n and Ang), TOMO(θ n)=tomo(Ang(i)), that is, this i data for projection corresponding to angle such as is at the slope data for projection.
In addition, described data for projection must be also the data for projection gathering under collimated beam radiation source, if radiation source is not collimated beam emissive source, should utilizes existing geometric transform method or utilize the fladellum of standard or cone-beam shuffle algorithm to be converted into collimated beam data for projection.
In step (2), described data for projection correction is comprised this data for projection is carried out to normalized, phase bit recovery, zero padding and registration.Wherein, described normalized in the prior art, refer to and utilize the background in n.s. region that the projection of different angles is carried out to background normalization, the present invention is on this basis by background area zero setting, and in all projections, same tomography carries out intensity normalization or all projections according to identical being normalized of whole object intensity.Described phase bit recovery refers to the propagation law according to light, design parameter during in conjunction with data for projection and experiment, the wavefront that detector position is obtained distributes and returns to the wavefront distribution at sample place, the effect of phase bit recovery is the enhancing of the margin signal of projection to be converted into the enhancing of interior of articles signal, contributes to reduce ground unrest simultaneously.The present embodiment is also expanded the application of phase bit recovery, is combined application with data for projection registration, has improved the degree of accuracy of prior art registration.Described zero padding refers to around object to be reconstructed or the zero padding around of whole data for projection, this operation contributes to the reconstruction of object and the recovery of missing data, described missing data is the projection angle that cannot get in acquisition process, or the data based on region outside experimental data in frequency domain space, this part data can be restored by interative computation below.In traditional filtered back projection reconstruction algorithm, without zero padding operation, the present embodiment adopts zero padding to contribute to improve the accuracy of subsequent registration.Described registration refers to all data for projection is modified to around the rotation of same axle center, and described axle center can be the object center of gravity of utilizing gravity model appoach to find, can be also the common axle center that utilizes cross-correlation method and other method for registering to find.The most frequently used in existing method for registering is cross-correlation method,, calculate the position of the related coefficient maximum of adjacent two Angles Projections and carry out registration, the present invention can also adopt new gravity model appoach to carry out registration, this gravity model appoach refers to asks center of gravity to angled two-dimensional projection, required center of gravity is considered as the center of gravity of three-dimensional body, and center of gravity is redefined as rotation center.
In step (3), described Fourier transform refers to conventional fast Fourier transform (FFT), fractional order Fast Fourier Transform (FFT) (FrFFT) or nonuniform fast Fourier transform (NUFFT).
In step (4), the present invention utilizes Fourier's theorem of cutting into slices that the frequency domain Conversion of Spatial Data under described polar coordinate system is become to the frequency domain spatial data under pseudo-polar coordinate system.
In step (5), described process of iteration refer to time frequency domain space under domain space and pseudo-polar coordinate system between iterative cycles computing, specifically comprise the following steps:
Step (51), carries out contrary pseudo-polar coordinates Fast Fourier Transform (FFT) to the frequency domain spatial data under described pseudo-polar coordinate system, so that it converts time domain spatial image to;
Step (52), judge whether to meet described default final condition, if met, carry out described step (6), otherwise, execution step (53), wherein, described final condition refers to predetermined iterations, or iterative process frequency domain space error function reaches the error amount of setting, or iterative process frequency domain space error no longer further significantly reduces.Described no longer significantly reduce be when time error of iteration and the error ratio of last iteration, its variation is no more than the value of setting.Described error function refers to the error function relatively obtaining between the data that calculate in the data of frequency domain space based on experiment and iterative process.Therefore, the image of output will be hour corresponding time domain space reconstruction image of frequency domain space error, or iterations reaches peaked reconstruction image;
Step (53), described time domain spatial image in described step (51) is carried out to time domain space constraints, so that this time domain spatial image is revised, described time domain space constraints comprises edge-restraint condition, Condition of Non-Negative Constrains, real number constraint condition, extreme value constraint condition and filtering.When described edge-restraint condition refers to, in domain space, have a border, being within the boundary is unknown image-region to be reconstructed, beyond border, is known region, and pixel value is zero; Described Condition of Non-Negative Constrains refers in the time domain spatial image that iterative process calculates, region outside border directly replaces with zero or its pixel value is approached to zero, and the pixel that within border, pixel value is negative value directly replaces with zero or its pixel value is approached to zero; Described real number constraint condition refers to that the pixel value of time domain spatial image is real number, while calculating plural number in iterative process, gets its real part or delivery; Described extreme value constraint condition refers to that the pixel value of rebuilding image can not be greater than a certain maximum value or can not be less than a certain minimal value, when the pixel value calculating is greater than maximum value or is less than minimal value, by maximum value or minimal value, replaces; Described filtering is that the time domain spatial image to calculating in iterative process carries out filtering noise reduction process;
Step (54), the described time domain spatial image that described step (53) is revised converts the frequency domain spatial data under pseudo-polar coordinate system to;
Step (55), frequency domain spatial data under described pseudo-polar coordinate system in described step (54) is carried out to frequency domain space constraints to revise, this frequency domain space constraints comprises constraint condition and/or the filtering based on experimental data, the described constraint condition based on experimental data is according to Fourier's theorem of cutting into slices, the corresponding frequency domain spatial data of data for projection that utilizes experiment to obtain is replaced the frequency domain spatial data calculating in iterative process, remainder data remains unchanged, wherein, the data based on experiment in the present invention refer to the time domain space projection data that arrive by detector direct-detection in step (1), described filtering is to carry out filtering noise reduction for the data based on region outside experimental data.
Wherein, in above-mentioned steps (54), conventionally adopt pseudo-polar coordinates Fast Fourier Transform (FFT) (PPFFT) to convert time domain spatial image to frequency domain spatial data under pseudo-polar coordinate system.Certainly, except directly adopting PPFFT conversion, can also adopt following steps to replace:
Step (541), calculates the data for projection of each projection angle according to described time domain spatial image, computing method are radon conversion or other Method of Projection Changes;
Step (542), revises the described data for projection in described step (541), comprises and utilizes the data for projection of experiment gained to replace the corresponding angle projection calculating, and all the other data for projection that calculate gained remain unchanged;
Step (543), the described data for projection that described step (542) is revised is carried out Fourier transform, so that it is converted to the frequency domain spatial data under polar coordinate system, wherein, Fourier transform herein can adopt Fast Fourier Transform (FFT), Nonuniform fast Fourier transform or Fourier Transform of Fractional Order;
Step (544), becomes the frequency domain spatial data under pseudo-polar coordinate system by the frequency domain Conversion of Spatial Data under the described polar coordinate system in described step (543), enters repeatedly band circulation next time.
It should be noted that, radon conversion will use interpolation algorithm, thereby example below 1, example 2 and example 3 all adopt pseudo-polar coordinates Fast Fourier Transform (FFT) (PPFFT) directly to convert time domain spatial image to frequency domain spatial data under pseudo-polar coordinate system in process of reconstruction, and do not adopt above-mentioned steps (541)-(544), thereby avoided use interpolation algorithm.
Below by example 1-3, verify the advantage that the present invention brings:
Example 1:
Shown in Fig. 5 A-5D, Fig. 5 A is that Fig. 5 B is the sinogram that utilizes collimated beam projection to obtain for simulating the former figure of reconstruction, and Fig. 5 C and Fig. 5 D are the reconstruction figure that utilizes the present invention to obtain.Former figure and reconstruction figure size are 512 * 512 pixels, and to simulate, in collimated beam projection process, to adopt image acquisition mode of the present invention, start angle be-45 degree, obtains altogether 128 angles.The edge-restraint condition that in the time of in image reconstruction process, domain space is used is the fixedly rectangular window of 376 * 408 pixels; Further, each time in iterative process, all pixel value zero setting beyond border, border is operating as with interior pixel value: when the pixel value of inferior iteration deducts the product of last iterated pixel value and adjustment factor, as the input value of next iteration, wherein adjustment factor is the decimal between 0-1.In the present embodiment, adjustment factor value is 0.9, and iterations is 20 times, take maximum iteration time as final condition in iteration, and reconstructed results is referring to Fig. 5 C.
When start angle is-40.156 degree, angle at the end is 129.629 degree, and all the other angles disappearance, obtains 108 angles altogether, during iterations 100 times, uses reconstructed results that image rebuilding method of the present invention obtains referring to Fig. 5 D.
Example 2:
Shown in Fig. 6 A-6B, Fig. 6 A is the reconstructed results of utilizing conventional filtered back projection (FBP) to obtain, and Fig. 6 B is the reconstructed results of utilizing image rebuilding method of the present invention to obtain.Laboratory sample is for solidifying concrete material, data for projection correction in step (2) comprises normalization, phase bit recovery, zero padding and registration, the theoretical formula list of references T.E.Gureyev of phase bit recovery wherein, T.J.Davis, A.Pogany, S.C.Mayo, S.W.Wilkins.Appl.Opt.43(12): 2418-2430(2004) and T.E.Gureyev, A.Pogany, D.M.Paganin, S.W.Wilkins.Opt.Commun.231(1-6): 53-70(2004).Registration adopts gravity model appoach to carry out registration, its theoretical formula list of references Chien-Chun Chen, Jianwei Miao, and T.K.Lee.PhysRevB.79(5) .052102(2009).Rebuilding image size is 1000 * 1000 pixels, the edge-restraint condition that in the time of in image reconstruction process, domain space is used is the fixedly rectangular window of 804 * 794 pixels, adjustment factor value is 0.9, and iterations is 20 times, take maximum iteration time as final condition in iteration.It is 1000 that FBP in Fig. 6 A rebuilds the projection number using, and the projection number that the reconstruction in Fig. 6 B is used is 250.From the result contrast of two kinds of methods, can find out, the present invention is when guaranteeing reconstruction quality, and the projection number of use greatly reduces.In Fig. 6 A and B, only shown that border rebuilds image with interior object.
Example 3:
Shown in Fig. 7 A-7C, Fig. 7 A is that Fig. 7 B is the sinogram that utilizes fladellum projection to obtain for simulating the former figure of reconstruction, and Fig. 7 C is the reconstruction figure that utilizes the present invention to obtain.Former figure and reconstruction figure size are 512 * 512 pixels, and for simulating the result that the data of fladellum radiation source institute projection are rebuild, start angle is-45 degree, obtains altogether 128 angles, the geometric center that rotation center is former figure.Step (1) comprises utilizes shuffle algorithm that fladellum projection is converted to collimated beam projection, the theoretical formula list of references Guy Besson.Medical Physics26(3 of shuffle algorithm): 415-426(1998).The edge-restraint condition that in the time of in image reconstruction process, domain space is used is the fixedly rectangular window of 371 * 450 pixels, and adjustment factor value is 0.9, and iterations is 20 times, take maximum iteration time as final condition in iteration.
Above-described, be only preferred embodiment of the present invention, not in order to limit scope of the present invention, the above embodiment of the present invention can also make a variety of changes.Be that simple, the equivalence that every claims according to the present patent application and description are done changes and modify, all fall into the claim protection domain of patent of the present invention.
Claims (16)
1. a low dosage CT image rebuilding method, is characterized in that, the method comprises the following steps:
Step (1), obtains the data for projection that waits slope delta of different projection angle θ;
Step (2), revises described data for projection;
Step (3), carries out Fourier transform to revised described data for projection, so that it converts the frequency domain spatial data under polar coordinate system to;
Step (4), becomes the frequency domain spatial data under pseudo-polar coordinate system by the frequency domain Conversion of Spatial Data under described polar coordinate system;
Step (5), by process of iteration make frequency domain space under pseudo-polar coordinate system of described frequency domain spatial data in described step (4) and time repeat conversion between domain space, until meet default final condition;
Step (6), time-domain diagram picture when output meets final condition.
2. low dosage CT image rebuilding method according to claim 1, is characterized in that, the described data for projection in described step (1) is the data by waiting slope incremental mode to obtain.
3. low dosage CT image rebuilding method according to claim 1, is characterized in that, the data that the described data for projection in described step (1) is the slope delta such as approximate that obtained and selected from the data of obtaining by equal angles incremental mode.
4. according to the low dosage CT image rebuilding method described in claim 2 or 3, it is characterized in that, the described projection angle θ in described step (1) meets following formula:
Wherein, the pixel that N * N is image to be reconstructed.
5. low dosage CT image rebuilding method according to claim 1, is characterized in that, the data of the described data for projection in described step (1) for gathering under collimated beam radiation source.
6. low dosage CT image rebuilding method according to claim 1, is characterized in that, the described data for projection in described step (1) for gathering and be converted to the data of parallel projection under fladellum or cone-beam radiation source.
7. low dosage CT image rebuilding method according to claim 6, is characterized in that, described step (1) comprises by shuffle algorithm, the data that gather are converted to the data of parallel projection under described fladellum or cone-beam radiation source.
8. low dosage CT image rebuilding method according to claim 1, is characterized in that, described step (2) realizes correction by described data for projection is carried out to normalization, zero padding, registration and/or phase place recovery operation.
9. low dosage CT image rebuilding method according to claim 1, is characterized in that, the described Fourier transform in described step (3) is Fast Fourier Transform (FFT), Nonuniform fast Fourier transform or Fourier Transform of Fractional Order.
10. low dosage CT image rebuilding method according to claim 1, is characterized in that, described step (5) comprises the following steps:
Step (51), carries out contrary pseudo-polar coordinates Fast Fourier Transform (FFT) to the frequency domain spatial data under described pseudo-polar coordinate system, so that it converts time domain spatial image to;
Step (52), judges whether to meet described default final condition, if met, carries out described step (6), otherwise, execution step (53);
Step (53), revises the described time domain spatial image in described step (51);
Step (54), the described time domain spatial image that described step (53) is revised converts the frequency domain spatial data under pseudo-polar coordinate system to;
Step (55), revises the frequency domain spatial data under the described pseudo-polar coordinate system in described step (54), then returns to step (51).
11. low dosage CT image rebuilding method according to claim 10, is characterized in that, described step (54) comprises carries out pseudo-polar coordinates Fast Fourier Transform (FFT) to described time domain spatial image.
12. low dosage CT image rebuilding methods according to claim 10, is characterized in that, described step (54) comprises the following steps:
Step (541), calculates the data for projection of each projection angle according to described time domain spatial image;
Step (542), revises the described data for projection in described step (541);
Step (543), the described data for projection that described step (542) is revised is carried out Fourier transform, so that it is converted to the frequency domain spatial data under polar coordinate system;
Step (544), becomes the frequency domain spatial data under pseudo-polar coordinate system by the frequency domain Conversion of Spatial Data under the described polar coordinate system in described step (543).
13. low dosage CT image rebuilding methods according to claim 12, is characterized in that, the described Fourier transform in described step (543) is Fast Fourier Transform (FFT), Nonuniform fast Fourier transform or Fourier Transform of Fractional Order.
14. low dosage CT image rebuilding methods according to claim 10, it is characterized in that, described step (53) is revised described time domain spatial image by exercise boundary constraint condition, Condition of Non-Negative Constrains, real number constraint condition, extreme value constraint condition and/or filtering.
15. low dosage CT image rebuilding methods according to claim 10, it is characterized in that, described step (55) is revised the frequency domain spatial data under described pseudo-polar coordinate system by constraint condition and the filtering carried out based on experimental data, wherein, the constraint condition of described execution based on experimental data is the frequency domain spatial data of the corresponding angle that calculates in the frequency domain spatial data replacement step (54) of utilizing under the corresponding pseudo-polar coordinate system of the data for projection obtaining in described step (1).
16. low dosage CT image rebuilding methods according to claim 15, is characterized in that, the described default final condition in described step (52) is at least one in following condition:
The maximum times of described step (5) circulation;
The numerical range of one image parameter;
The minimum value of error function; And
Described error function no longer reduces with iterations increase,
Wherein, described error function is frequency domain spatial data under the described pseudo-polar coordinate system calculating in described step (54) the resulting error function of comparing with the frequency domain spatial data under the corresponding pseudo-polar coordinate system of data for projection of obtaining in described step (1).
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